Analytical and Numerical Modeling of Delamination Evolution in Fiber Reinforced Laminated Composites Subject to Flexural Loading

Abstract

Delamination is a common failure mode in composite (fiber reinforced and layered) structures subject to low-velocity impacts by foreign objects. To maximize the design capacity, it is important to have reliable tools to predict delamination evolution in laminated composites. The focus of this research is to analyze flexural responses and delamination evolution in laminated composites subject to flexural loading. Analytical solutions were derived from linear elasticity theory and structural mechanics of beam and plate configurations. Formulations and evaluations of the proposed analytical approaches were validated by comparing with results of finite element (FE) simulations in similar settings and published experiment data. Two-dimensional (2D) elasticity theory for laminated panels was extended to analyze elastodynamic responses of pristine panels and quasi-static responses of pre-delaminated panels. A highlight of the approach is exact solutions of displacement and stress fields it provides. Further investigations showed that the 2D elasticity theory is not amenable to a closed-form solution for laminates containing off-axis angle plies due to three-dimensional (3D) states of stress. Closed-form solutions of cohesive zone modeling (CZM) were developed for popular delamination toughness tests of laminated beams. A laminate was modeled as an assembly of two sub-laminates connected by a virtual deformable layer with infinitesimal thickness. Comprehensive parametric studies were performed, offering a deeper understanding of CZM. The studies were further simplified so that closed-form expressions can be obtained, serving as a quick estimation of the flexural responses and the process zone lengths. Analytical CZM solutions were extended analyze quasi-static impact tests of laminated composite plates with arbitrary stacking sequences, aiming to predict critical load, critical interfaces and extent of delamination at that interface. The Rayleigh-Ritz method was used to determine approximate solutions. The predicted results were found in good agreement with FE simulations.